Question: Simplify the following expression: $\dfrac{120k^3}{80k^3}$ You can assume $k \neq 0$.
Answer: $ \dfrac{120k^3}{80k^3} = \dfrac{120}{80} \cdot \dfrac{k^3}{k^3} $ To simplify $\frac{120}{80}$ , find the greatest common factor (GCD) of $120$ and $80$ $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $80 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(120, 80) = 2 \cdot 2 \cdot 2 \cdot 5 = 40 $ $ \dfrac{120}{80} \cdot \dfrac{k^3}{k^3} = \dfrac{40 \cdot 3}{40 \cdot 2} \cdot \dfrac{k^3}{k^3} $ $\phantom{ \dfrac{120}{80} \cdot \dfrac{3}{3}} = \dfrac{3}{2} \cdot \dfrac{k^3}{k^3} $ $ \dfrac{k^3}{k^3} = \dfrac{k \cdot k \cdot k}{k \cdot k \cdot k} = 1 $ $ \dfrac{3}{2} \cdot 1 = \dfrac{3}{2} $